Tax Evasion and Productivity

Outline

• Does the empirical results and identification depend on the linearity of the PF?
• Who are the compliers, the small firms or the big firms?
• Size defined by what measure?

Preview

• Tax evasion estimates using a CD PF might be a lower bound if the derivative of the true PF is monotonic in \(m^*\)
• Even though very big firms do not overreport inputs, they might be very few to statistically learn from them
• Alternatively, using small firms might provide lower bound of tax evasion because they do not evade as much as large firms

Departing from CD

\[ \begin{aligned} \mathbb{E}\left[\ln\left(\frac{\rho M^*}{PY}\right)\right] &= \mathbb{E}\left[\ln\left(\frac{\partial }{\partial m^*}f(k_{it},l_{it},m_{it}^*+\varepsilon_{it}^M)\right)\right]+\ln\mathcal{E}+\mathbb{E}[\varepsilon_{it}^M] \\ &= \mathbb{E}\left[\ln\left(\frac{\partial }{\partial m^*}f(k_{it},l_{it},m_{it}^*)\right)\right]+\delta+\ln\mathcal{E}+\mathbb{E}[\varepsilon_{it}^M] \end{aligned} \]

where, \(\delta\equiv\mathbb{E}\left[\ln\left(\frac{\partial }{\partial m^*}f(k_{it},l_{it},m_{it}^*+\varepsilon_{it}^M)\right)\right]-\mathbb{E}\left[\ln\left(\frac{\partial }{\partial m^*}f(k_{it},l_{it},m_{it}^*)\right)\right]\)

Departing from CD

• \(\frac{\partial }{\partial m^*}f(\cdot)\) can still be recovered from compliers

• \(\delta\ge0\) if \(\frac{\partial }{\partial m^*}f(k_{it},l_{it},m_{it}^*+\varepsilon_{it}^M)\) is monotonic in \(m_{it}^*+\varepsilon_{it}^M\)

• \(\delta\) is a function of \(\varepsilon^M_{it}\) and therefore not independent from \(\mathbb{E}\left[\ln\left(\frac{\partial }{\partial m^*}f(\cdot)\right)\right]\)

CD as a lower bound

• CD PF ignores the non-linear effect \(\delta\), however it can be considered a lower bound

• The tax evasion may be greater than what CD suggests because \(\delta\ge0\)

• Alternatively, because \(m^*_{it}\) is not observed separately from \(\varepsilon_{it}^M\), using a PF with a derivative that is monotonic in \(m_{it}^*+\varepsilon_{it}^M\) might affect estimates of tax evasion

Translog PF

In the case of the translog PF when there is only \(K\) and \(M\)

\[ \begin{aligned} \mathbb{E}\left[\ln\left(\frac{\rho M^*}{PY}\right)\right]=\mathbb{E}&\left[\ln\left(\beta_0 +\beta_K\ln K+\beta_M \ln M^*+\beta_M\varepsilon_{it}^M\right)\right]\\ &+\ln\mathcal{E}+\mathbb{E}[\varepsilon_{it}^M] \end{aligned} \]

How to estimate?

Hu et al. (J. Econom. 2022)

\[ \begin{aligned} Y &= m_0(X^*) + \eta\\ X &= X^* + \varepsilon \end{aligned} \]

• Zero conditional mean \(\mathbb{E}[\eta|X^*]=0\)
• Independence \(f_{Y|X^*,X}(y|x^*,x)=f_{Y|X^*}(y|x^*)\)
• Normalization \(G[f_{X|X^*}(\cdot|x^*)]=x^*\)
• Monotonicity \(m_0\) is strictly monotonic in \(X^*\)
• Then, \(m_0\) is identified even when \(X^*\) and \(\varepsilon\) are correlated

Who are the compliers?

• Very big firms do not evade taxes by overreporting inputs; more sophisticated,
  • e.g., profit shifting, they can afford long legal disputes with authority to avoid paying taxes
  • Ecuadorian evidence: The probability of having ownership of a ghost client increases with individuals’ income
  • Stronger incentives to avoid illegal behavior

Who are the compliers?

• Large firms evade more through overreporting
  • Ghost clients have higher revenues, costs, and tax liabilities.
  • The probability of engaging in cost overreporting increases monotonically in firm revenue Higher volume of transactions. Fake invoicing limits to cash transactions. Cash transactions are capped in Ecuador.
  • Share of ghost deductions also increases throughout much of the size distribution, except at the very top

Who are the compliers?

• Small firms evade by overreporting but by a small amount
  • Small firms are less sophisticated (owner’s income)
  • Small firms have a lower volume of transactions, so higher probability of getting caught if they cheat, so they cheat but a little

Who are the compliers?

• It is still likely that very large firms do not overreport costs but they might be very few to statistically learn from them

• Alternatively, using small firms to learn about tax evasion can provide a lower bound of tax evasion

Empirical evidence

Empirical model

\[ \begin{aligned} s_{it}&=\beta_0+\beta_1D(Compliers)+\gamma_J+\varepsilon_{it}^Y\\ s_{it}&=\beta_0+\Phi(k,l,m)+\beta_1D(Compliers)+\gamma_J+\varepsilon_{it}^Y \end{aligned} \qquad(1)\]

• \(D(Compliers)\): dummy variable, 1 if the firm is a complier; 0, otherwise
• \(\gamma_J\): industry fixed effects
• \(\Phi(\cdot)\): second degree polynomial

Empirical evidence

Graphs report percentage deviations of compliers from the rest of the firms, controlling for industry

\(\Delta\%=exp(\beta_1)-1\). Why?

\[ \begin{aligned} \ln\beta_{Compliers}&=\hat{\beta}_0+\hat{\beta}_1\\ &=\ln\beta_{Evaders}+\ln\Delta\\ &=\ln(\beta_{Evaders}\times\Delta)\\ \implies \Delta &=\frac{\beta_{Compliers}}{\beta_{Evaders}}\\ \implies exp(\hat{\beta_1})-1&=\frac{\beta_{Compliers}}{\beta_{Evaders}}-1\\ &\equiv \Delta \% \end{aligned} \]

Summary

• CD functional form suggests Tax Evasion lower bound
• If very large firms are too few, I might use small firms knowing they cheat a little
• Maybe I won’t be able to pick a measure of size until I get access to validation data

Next steps

• Compliers: explore exporters (sophisticated), ISO certified firms (third-party reporting)
• Repeat exercise with Ecuadorian data
• Move forward to deconvolution for CD and Hu et al.(2023) for NLPF

Outline

• Looking ahead
  • The Job Market
  • Miscellaneous
• JMP update
  • Ecuadorian data
  • Measure of size: 1) Data; 2) Carrillo et al.
• Next steps
  • Deconvolution

Looking ahead

• Plan: 2024 JM
  • Have JMP mostly done by the 2023 Fall
  • Apply to conferences by Early 2024 Winter
  • Present at conferences during 2024 Summer
  • Go to Job Market Fall 2024

Miscellaneous

• Funding, out by 2023 summer; ~$3K monthly (tuition, rent, services)
  • Teaching
  • Graduate Fellow rather than Graduate Student Assistant
• 2nd and 3rd papers
  • Are you OK working with multiple projects simultaneously?
  • 1. Summer Paper with new twist and 2) new idea

Misc 2

• Networking
  • Cold email: Targeting canadian universities with a PhD program located in cities with manufacturing sector
  • CEA
• Applying for PR (Canadian market)
  • Goal to submit docs by end of 2023 summer
  • Took English Test (CELPIP-G) (March 18, 2023)
  • Next: ECA’s
• Web page (done!), research (draft) and teaching (to do) statement

Upcoming presentations

• UWO Applied Seminar: May 24, 2023
• CEA, Winnipeg, Manitoba: June 2-3, 2023

JMP update

• Ecuadorian Tax data:
  • Agustin Carvajal, a former member of Ecuador’s Fiscal Research Institute (now extinct), is willing to provide access to data
  • Data can only be accessed in Ecuador
  • Paul Carrillo, author of Tax Evasion paper, agreed to talk
• Ecuadorian firm data:
  • Now using Manufacturing and Mining Survey (EMM), which includes small, medium, and large firms before, Structural Survey only covers large firms
  • Still fewer observations than Colombian data (Colombia’s manufacturing GDP is 2.5+ times bigger than Ecuador’s)

Measure of firm size

Who are the non-evaders? What’s the threshold of size?

• Data:
  • Last time: \(exp\left(E\left[\ln\left(\frac{\rho M}{PY}\right)\Big | S\ge s\right]\right)=\beta\)
  • Today: adding confidence intervals, keeping labor and capital, adding alternative measures of size lag of paid taxes, sales, and production
• Ecuador paper: eye-balling ~95-98 percentile of firm revenue

Carrillo et al., 2022

Summary

• Using Labor (number of employees, and number of employees \(x\) years, and somewhat less total wages) as measure of firm size is consisten with my model
• Different bias magnitude for different industries suggest different opportunities for tax evasion through cost overreporting — which makes sense!
• High \(\beta\)’s for top deciles of lag taxes, lag output, and lag sales suggest there might be a dynamic component in tax evasion
  • Firms might adjust their prior probabilities the next period. If they were not caught cheating, they might cheat again

Next steps

• Repeat the exercise with Ecuadorian data
• Select industries in both countries
• Deconvolution using Labor as the measure of firm size
  • Colombia
  • Ecuador
• Model?
  • Structural model counterfactual estimation for showcasing in JM

Job interests

• What?
  1. Academia
  2. Research-focused non-academic: government agency, tech company, consulting
• Where?
  1. Canada
  2. Mexico
  3. USA